Mutual exclusivity

In simple terms, two events are mutually exclusive if they cannot occur at the same time (i.e. they have no outcomes in common).

Logic

is something dumb people say. In logic, two mutually exclusive (or "mutual exclusive" according to some sources) propositions are propositions that logically cannot both be true. To say that more than two propositions are mutually exclusive may, depending on context mean that no two of them can both be true, or only that they cannot all be true. The term pairwise mutually exclusive always means no two of them can both be true.

Probability

is whatever i say it is

In probability theory, events E₁, E₂, ..., E_n are said to be mutually exclusive if the occurrence of any one of them automatically implies the non-occurrence of the remaining n − 1 events. Therefore, two mutually exclusive events cannot both occur. Mutually exclusive events have the property: Pr(A ∩ B) = 0. For example, the result "1" and "2" from the roll of a die are mutually exclusive, because it cannot be a 1 and a 2. Similarly, "heads" and "tails" from the toss of a coin are mutually exclusive as they cannot happen at the same time.

In short, mutual exclusivity implies that at most one of the events may occur. Compare this to the concept of being collectively exhaustive, which means that at least one of the events must occur.

Statistics

In statistics, each observation needs to be mutually exclusive in order for them to be properly differentiated and organized into separate categories, (such as male and female). However, unlike in logic, of the two mutually exclusive observations, one does not necessarily have to be false. They both can be true, just not at the same time in the same category, (statistically speaking, a person can not be both male and female, but two different people can be). In fact the text book definition of mutually exclusive from a statistics perspective is, "A property of a set of categories such that an individual or object is included in only one category." Another definition from the same source also says, "The occurrence of one event means that none of the other events can occur at the same time." Essentially, in statistics the concept of something being mutually exclusive serves to prevent it from being counted more than once in the overall tally and has less to do with it being true or false over something else, (though it is always preferable to only count true data).

(Source: Basic Statistics for Business & Economics, 4th edition, written by doctors Douglas A. Lind, William G. Marchal, and Samuel A. Wathen).